Finite Group Databasebeta

← #44507398

Subgroups — #44507398

Order 30848.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21440687C211yesmaximal, characteristic
2C2×#21440570C212yesmaximal, complemented
3#29507716C212yesmaximal, complemented
4C2×#21440559C211yesmaximal, characteristic, complemented
5#390×C241C211yesmaximal, characteristic, complemented
6#21440687—24no—
7#21440687—22no—
8#21440687C414yescomplemented
9C2×#16838770C2212yes—
10C2×#16838769—22no—
11C22×C22⋊D241—22no—
12C2×D4×D241—22no—
13C2×#16838754C2212yescomplemented
14#21440570—24no—
15#21440565—22no—
16#21440562—22no—
17#21440559—22no—
18C22×D4×C241C2211yescharacteristic
19C2×C4⋊C4×C241C2211yescharacteristic, complemented
20C2×C22⋊C4×C241—22no—
21C2×C42×C241C2211yescharacteristic, complemented
22C23×D241—22no—
23#16838770—22no—
24#16838770—22no—
25#16838770C2×C414yes—
26#16838770D414yes—
27#16838769—28no—
28#16838769—28no—
29C2×Dic482D412yes—
30C2×D964D412yes—
31C2×C22⋊D241—24no—
32C2×C22⋊D241—28no—
33C2×C22⋊D241—28no—
34C2×C22⋊D241—22no—
35D4×D241—28no—
36D4×D241—28no—
37C22×Dic241—22no—
38C2×C4×D241—22no—
39#16838754—22no—
40#16838754—22no—
41C2×#14515349—22no—
42C24×C241D412yes—
43C2×D4×C241—22no—
44C2×D4×C241—22no—
45C2×D4×C241C2×C412yes—
46C2×D4×C241D412yes—
47C22×C4×C241—21no—
48C22×C4×C241—21no—
49C22×C4×C241C2311yescharacteristic
50C4⋊C4×C241—22no—
51C22⋊C4×C241—44no—
52C42×C241—22no—
53C22×D241—22no—
54C22×D241—28no—
55C22×D241—82no—
56C22×D241—82no—
57Dic482—22no—
58Dic482C22⋊C414yescomplemented
59D964—22no—
60D964C22⋊C414yescomplemented
61C22⋊D241—216no—
62C22⋊D241—24no—
63C22⋊D241—24no—
64C2×Dic241—28no—
65C2×Dic241—22no—
66C4×D241—24no—
67C4×D241—24no—
68#14515349—42no—
69C23×C241—22no—
70C23×C241—22no—
71C23×C241—42no—
72C23×C241—42no—
73C23×C241C22⋊C414yes—
74C23×C241C2×D411yescharacteristic
75D4×C241—24no—
76D4×C241—24no—
77C2×C4×C241—22no—
78C2×C4×C241—41no—
79C2×C4×C241—41no—
80C2×C4×C241—42no—
81C2×C4×C241—41no—
82C2×C4×C241C22×C411yescharacteristic
83C2×C4×C241C2×D412yes—
84C2×C4×C241C2×D412yes—
85C2×C4×C241C2×D411yescharacteristic
86C22×C241—21no—
87C22×C241—21no—
88C22×C241—24no—
89C22×C241—44no—
90C22×C241—42no—
91C22×C241—42no—
92C22×C241—82no—
93C22×C241C2×C22⋊C411yescharacteristic
94C22×C241#12011yescharacteristic
95C22×C241#12011yescharacteristic
96C2×D241—24no—
97C2×D241—42no—
98C2×D241—42no—
99C2×D241—88no—
100C4×C241—42no—
101C4×C241—81no—
102C4×C241C2×C22⋊C412yes—
103C4×C241#12012yes—
104Dic241—24no—
105C2×C241—21no—
106C2×C241—21no—
107C2×C241—44no—
108C2×C241#37911yescharacteristic
109C2×C241#45311yescharacteristic
110C2×C241#45511yescharacteristic
111D241—44no—
112C241#179211yescharacteristic, complemented, Sylow
113#1792—2411nomaximal, Sylow
114C2×H(5,𝔽2)—2411no—
115C2×#104—2412no—
116#417—2412no—
117C2×#100—2411no—
118#390D24111yescharacteristic, complemented
119H(5,𝔽2)—4824no—
120H(5,𝔽2)—4822no—
121H(5,𝔽2)—2414no—
122C2×#41—4822no—
123C2×#41—2412no—
124C22×D4—4822no—
125C22×D4—4822no—
126C22×D4C2×D24111yescharacteristic
127C2×M16—2412no—
128C2×C4⋊C4C2×D24111yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D24111yescharacteristic, complemented
131#104—4824no—
132#103—4822no—
133#102—4822no—
134#100—4822no—
135C24—4822no—
136C24C22⋊D24112yes—
137#41—4828no—
138#41—4828no—
139#41—4822no—
140#41—4822no—
141#41—2414no—
142#41—2414no—
143C2×Q8—2412no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—4828no—
147C2×D4—4828no—
148C2×D4—4824no—
149C2×D4—4828no—
150C2×D4—4828no—
151C2×D4—4822no—
152C2×D4—2412no—
153C2×D4C4×D24112yes—
154C2×D4D96412yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—4822no—
158C22×C4—4822no—
159C22×C4C22×D24111yescharacteristic
160M16—4822no—
161M16—4822no—
162C2×C8—4822no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—19282no—
171C23—19282no—
172C23—4828no—
173C23—4822no—
174C23#1683874714yes—
175C23C2×C22⋊D24111yescharacteristic
176Q8—4822no—
177Q8—2414no—
178D4—24no—
179D4—24no—
180D4—48216no—
181D4—4824no—
182D4—4824no—
183D4—4822no—
184D4—2414no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—4828no—
191C2×C4—4822no—
192C2×C4—4824no—
193C2×C4—4824no—
194C2×C4C2×C4×D24111yescharacteristic
195C2×C4D4×D24112yes—
196C2×C4D4×D24112yes—
197C2×C4C2×D96411yescharacteristic
198C8—9642no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—19288no—
207C22—9642no—
208C22—9642no—
209C22—4824no—
210C22C2×#1683874711yescharacteristic
211C22#2144061011yescharacteristic
212C22#2144061011yescharacteristic
213C4—42no—
214C4—81no—
215C4—4824no—
216C4C22⋊C4×D24112yes—
217C4#2144061212yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—9644no—
222C2#2950757211yescharacteristic
223C2#2950788411yescharacteristic
224C2#2950789411yescharacteristic
subgroupG/H
centerC22#21440610
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#390×C241C2
socleC22×C241#120
prime radicalC2×#21440687C2
cosocleC22×C4×C241C23
hypercenter#390D241
hypocenterC241#1792
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#21440570C2semidirect
3. #29507716C2semidirect
4. C2×#21440559C2semidirect
5. #390×C241C2semidirect
8. #21440687C4semidirect
13. C2×#16838754C22semidirect
19. C2×C4⋊C4×C241C22semidirect
21. C2×C42×C241C22semidirect
58. Dic482C22⋊C4semidirect
60. D964C22⋊C4semidirect
112. C241#1792semidirect
118. #390D241semidirect
128. C2×C4⋊C4C2×D241semidirect
130. C2×C42C2×D241semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#214406872
C2×#214405702
#295077162
C2×#214405592
#390×C2412
#1792241